1

GATE ME 2017 Set 1

MCQ (Single Correct Answer)

+2

-0.6

$$\,\,P\,\,\,\left( {0,3} \right),\,\,Q\,\,\,\left( {0.5,4} \right),\,\,$$ and $$\,\,R\,\,\,\left( {1,5} \right)\,\,\,$$ are three points on the curve defined by $$\,\,f\left( x \right),\,\,$$ Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits $$x=0$$ and $$x=1$$ for the curve. The difference between the two results will be

2

GATE ME 2016 Set 2

Numerical

+2

-0

The error in numerically computing the integral $$\,\int\limits_0^\pi {\left( {\sin \,x + \cos \,x} \right)dx\,\,\,} $$ using the trapezoidal rule with three intervals of equal length between $$0$$ and $$\pi $$ is _________.

Your input ____

3

GATE ME 2016 Set 1

Numerical

+2

-0

Solve the equation $$x = 10\,\cos \,\left( x \right)$$ using the Newton-Raphson method. The initial guess is $$x = {\pi \over 4}.$$ The value of the predicted root after the first iteration, up to second decimal, is _____________.

Your input ____

4

GATE ME 2016 Set 1

Numerical

+2

-0

Gauss-Seidel method is used to solve the following equations (as per the given order).
$$${x_1} + 2{x_2} + 3{x_3} = 5$$$
$$$2{x_1} + 3{x_2} + {x_3} = 1$$$
$$$\,3{x_1} + 2{x_2} + {x_3} = 3$$$

Assuming initial guess as $${x_1} = {x_2} = {x_3} = 0,$$ the value of $${x_3}$$ after the first iteration is __________.

Assuming initial guess as $${x_1} = {x_2} = {x_3} = 0,$$ the value of $${x_3}$$ after the first iteration is __________.

Your input ____

Questions Asked from Numerical Methods (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE ME Subjects

Engineering Mechanics

Strength of Materials

Theory of Machines

Engineering Mathematics

Machine Design

Fluid Mechanics

Turbo Machinery

Heat Transfer

Thermodynamics

Production Engineering

Industrial Engineering

General Aptitude